Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations

Date

2014-12-15

Author

Akman, Tugba
Karasözen, Bülent

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In this paper, the distributed optimal control problem governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We investigate the commutativity properties of the optimize-then-discretize and discretize-then-optimize approaches for the continuous and discontinuous Galerkin time discretization. A priori error estimates are derived for fully-discrete state, adjoint and control. The numerical results given for convection dominated problems via optimize-then-discretize approach confirm the theoretically observed convergence rates.

Subject Keywords

Optimal control problems, Unsteady diffusion-convection-reaction equation, Variational time discretization, A priori error estimates

URI

https://hdl.handle.net/11511/31155

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2014.05.002

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

T. Akman and B. Karasözen, “Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 41–56, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31155.